The Mercator projection isn't a good example of a map in which visual distortion and a lack of navigational utility go hand in hand.
Indeed, the hole point of the projection was to make navigation easier by allowing rhumb lines (the shortest distances between two points on a curved surface) to be charted as perfectly straight lines on a two-dimensional map. From these lines of constant bearing, mariners could work out the precise - and constant - angle they should maintain in relation to the pole star in order to get from one point to another.
Without a reliable method for establishing longitude at sea, 17th Century navigators could never be exactly sure how far along their courses they were, but at least they could know that they were heading in the right direction. Given the level of uncertainty involved in these enterprises, this one piece of (relatively) hard and verifiable data was extraordinarily important, making the accuracy of the projection, and the mathematically - if not visually - correct placement of shorelines within it especially important.
Unfortunately, the iconic value of the Mercator projection has vastly outlived its utility - or at least, the common awareness of the once formidable navigational problems it addressed. Far from seeing it as a brilliant technical solution, it is often seen through a purely political filter that views its strengths as weaknesses, while completely missing the map's actual intent.
Let's not get mixed up about what the projection did and didn't do. As you point out, the importance of rhumb lines comes not from the fact that the thing they keep constant -- the bearing (with respect to north/south) -- was something that could actually be measured.
Rhumb lines are not, however, the shortest distance between two points on a sphere. Those would be great circles. In particular, note that along a rhumb line one can never reach the north or south pole. Indeed, rhumb lines are dependent on your choice of poles, which the actual shortest course clearly cannot be!
Argh. Misnegation from earlier version. "As you point out, the importance of rhumb lines comes from the fact that..." -- there shouldnt' be a not there.
You are (it seems intentionally) ignoring the point that Mercator's area distortion doesn't dangerously mislead in navigation, quite the contrary. Or, if that isn't true, please name some cases where navigators were messed up because they thought Greenland looked bigger than it was in area.
Unless you use a globe, every projection onto a flat rectangular surface distorts.
Now how does that make more plausible the claim that world map makers are inflating the area of Taiwan on purpose?
Really? Seemed like he was simply pointing out an error on my part. Don't see where Taiwan enters that at all.
More to the point, there's a big difference between distorting scale in a way that's mathematically consistent throughout the projection (i.e. one in which you preserve shape or position at scale's expense), and simply fudging the scale in a particular spot.
Really? I think you meant rhumb lines. :) They're both important, just for different reasons; and it's rhumb lines that are easily visible on a Mercator projection and that were so useful for navigation.
Indeed, the hole point of the projection was to make navigation easier by allowing rhumb lines (the shortest distances between two points on a curved surface) to be charted as perfectly straight lines on a two-dimensional map. From these lines of constant bearing, mariners could work out the precise - and constant - angle they should maintain in relation to the pole star in order to get from one point to another.
Without a reliable method for establishing longitude at sea, 17th Century navigators could never be exactly sure how far along their courses they were, but at least they could know that they were heading in the right direction. Given the level of uncertainty involved in these enterprises, this one piece of (relatively) hard and verifiable data was extraordinarily important, making the accuracy of the projection, and the mathematically - if not visually - correct placement of shorelines within it especially important.
Unfortunately, the iconic value of the Mercator projection has vastly outlived its utility - or at least, the common awareness of the once formidable navigational problems it addressed. Far from seeing it as a brilliant technical solution, it is often seen through a purely political filter that views its strengths as weaknesses, while completely missing the map's actual intent.